Question:
Let $f(x)=x .\left[\frac{x}{2}\right]$, for $-10
Solution:
We know $[x]$ discontinuous for $x \in Z$
$f(x)=x\left[\frac{x}{2}\right]$ may be discontinuous where $\frac{x}{2}$ is an
integer.
So, points of discontinuity are,
$x=\pm 2, \pm 4, \pm 6, \pm 8$ and 0
but at $x=0$
$\lim _{x \rightarrow 0^{+}} f(x)=0=f(0)=\lim _{x \rightarrow 0^{-}} f(x)$
So, $f(x)$ will be discontinuous at $x=\pm 2, \pm 4, \pm 6$ and $\pm 8$.
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